A064401 Numbers k such that k! - prime(k) is prime.

4, 5, 7, 12, 14, 15, 16, 17, 18, 20, 30, 37, 39, 49, 52, 66, 86, 162, 165, 202, 235, 250, 366, 419, 1169, 1311, 1916, 3032, 3211, 3335, 4650, 6199, 7762, 12776

Offset: 1

Author

Robert G. Wilson v, Sep 28 2001

Keywords

• nonn
• hard
• more

Comments

a(34) > 12500. - Giovanni Resta, Mar 16 2014

Crossrefs

Cf. A064278.

Programs

Magma

[n: n in [1..200] | IsPrime(Factorial(n)- NthPrime(n))]; // Vincenzo Librandi, Mar 05 2015

Mathematica

Do[ If[ PrimeQ[ n! - Prime[ n ] ], Print[ n ] ], {n, 1, 600} ]
Select[Range[2000], PrimeQ[#! - Prime[#]] &] (* Vincenzo Librandi, Mar 05 2015 *)

Extensions

a(25)-a(27) from Farideh Firoozbakht, Feb 28 2004

a(28)-a(33) from Giovanni Resta, Mar 16 2014

a(34) from Michael S. Branicky, Apr 20 2025